Related papers: Maximising common fixtures in a round robin tourna…
We describe a class of combinatorial design problems which typically occur in professional sailing league competitions. We discuss connections to resolvable block designs and equitable coverings and to scheduling problems in operations…
It is well known that a tournament (complete oriented graph) on $n$ vertices has at most ${1/4}\binom{n}{3}$ directed triangles, and that the constant 1/4 is best possible. Motivated by some geometric considerations, our aim in this paper…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
We consider a problem introduced by Feige, Gamarnik, Neeman, R\'acz and Tetali [2020], that of finding a large clique in a random graph $G\sim G(n,\frac{1}{2})$, where the graph $G$ is accessible by queries to entries of its adjacency…
Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…
This paper addresses the problem of scheduling jobs on identical machines with conflict constraints, where certain jobs cannot be scheduled simultaneously on different machines. We focus on the case where conflicts can be represented by a…
We consider the manipulability of tournament rules which map the results of $\binom{n}{2}$ pairwise matches and select a winner. Prior work designs simple tournament rules such that no pair of teams can manipulate the outcome of their match…
The game of memory is played with a deck of n pairs of cards. The cards in each pair are identical. The deck is shuffled and the cards laid face down. A move consists of flipping over first one card then another. The cards are removed from…
In this note, we extend a recent result on the uniqueness of the maximum score in a classical round-robin tournament to general round-robin tournament models with equally strong players, where the scores take values in $[0,\,1]$.
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
The matching game is a cooperative game where the value of every coalition is the maximum revenue of players in the coalition can make by forming pairwise disjoint partners. The multiple partners matching game generalizes the matching game…
We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that…
This paper takes a game theoretical approach to open shop scheduling problems with unit execution times to minimize the sum of completion times. By supposing an initial schedule and associating each job (consisting in a number of…
A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population…
Suppose that all groups of order $n$ are defined on the same set $G$ of cardinality $n$, and let the \emph{distance} of two groups of order $n$ be the number of pairs $(a,b)\in G\times G$ where the two group operations differ. Given a group…
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…
In many practical scenarios, a population is divided into disjoint groups for better administration, e.g., electorates into political districts, employees into departments, students into school districts, and so on. However, grouping people…
We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…
We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…
In a distributed game we imagine a team Player engaging a team Opponent in a distributed fashion. Such games and their strategies have been formalised in concurrent games based on event structures. However there are limitations in founding…